Question: Simplify the following expression: $y = \dfrac{6n^2 + 6n - 180}{n - 5} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ y =\dfrac{6(n^2 + 1n - 30)}{n - 5} $ Then we factor the remaining polynomial: $n^2 + {1}n {-30} $ ${-5} + {6} = {1}$ ${-5} \times {6} = {-30}$ $ (n {-5}) (n + {6}) $ This gives us a factored expression: $\dfrac{6(n {-5}) (n + {6})}{n - 5}$ We can divide the numerator and denominator by $(n + 5)$ on condition that $n \neq 5$ Therefore $y = 6(n + 6); n \neq 5$